Hi Judy,
Thanks for reaching out. As per your query, fonts are showing active in the Creative Cloud Desktop app (Image 1) but not in Illustrator Font Menu (Image 2).

If yes, please try the following steps:
- Log out of creative cloud through Illustrator.

- Shut down Illustrator
- Go to the Creative Cloud and Manage Fonts.

- Deactivate & Reactivate font

- Restart Illustrator and check again
Regards,
Srishti